3/2x+6+x+4+1/2x=25

Solution for 3/2x+6+x+4+1/2x=25 equation:

3/2x+6+x+4+1/2x=25

We move all terms to the left:

3/2x+6+x+4+1/2x-(25)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

x+3/2x+1/2x-15=0

We multiply all the terms by the denominator


x*2x-15*2x+3+1=0

We add all the numbers together, and all the variables

x*2x-15*2x+4=0

Wy multiply elements

2x^2-30x+4=0

a = 2; b = -30; c = +4;
Δ = b2-4ac
Δ = -302-4·2·4
Δ = 868
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{868}=\sqrt{4*217}=\sqrt{4}*\sqrt{217}=2\sqrt{217}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{217}}{2*2}=\frac{30-2\sqrt{217}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{217}}{2*2}=\frac{30+2\sqrt{217}}{4}
$